Grishka, the earliest I have seen is this one published in 1952, and also sung by Edric Connor in that year.
Nothing new, but for the record:

Lyr. Add: CUDELIA BROWN

Oh Cudelia Brown,
Wa meck yuh head so red?
(Yuh head so red)
Oh Cudelia Brown,
Wa meck yuh head so red?
(Yuh head so red)
Yuh sidung eena sunshine-
Wid nutten pon yuh head,
Oh Cudelia Brown,-
Das why yuh head so red!
(Yuh head so red)

On a moonshine night
I meet Missa Ivan,-
An' Missa Ivan tol' me,
Sey dat him gi' Netta de drop,
Jamaica flop an' de moonshine drop.
Ee-hee ha ha!
Ee-hee ha ha!
Ee-hee ha ha!

With musical score and guitar chords. Pp. 92-94.

Tom Murray, 1952, Folk Songs of Jamaica, Oxford University Press, London.
Reprinted in Jim Morse, 1958, Folk Songs of the Caribbean, Bantam Books, New York.

Morse gives no explanation, other than it is a humorous ditty; I have not seen the Murray book.

I can't relate the second verse to the first, it almost seems like it is from a second song. I will check Walter Jekyll for any similar verses, but 'Cudelia' does not appear in his 1904 book.

Yes, the 'Brown' could be ironic; I still have a feeling that Cudelia was light-skined, mixed, as I speculated before.
These shades were important in Jamaica (as elsewhere) and the newspaper, The Gleaner, printed in Jamaica, recently had an article warning Jamaican women from using face bleaches that were dangerous (Also several medical articles on the net saying that use of these bleaches was a serious problem in Jamaica).

Dunno. The song is unclear, and I am only speculating without foundation.